Statistical Mechanics, Molecular Modeling, and the Notion of Stress

An Invited Collection
2010
ISBN: 978-94-007-9010-0
Verlag: Springer Netherlands

Buch, Englisch, 153 Seiten, Paperback, Format (B × H): 155 mm x 235 mm, Gewicht: 254 g

The paper of Admal & Tadmor, “A Uni ed Interpretation of Stress in Molecular S- tems,” takes up the various existing microscopic de nitions of the Cauchy stress tensor. Here the ambition is to establish a unifying framework in which all of these molecular surfacial interactions can be derived and the connections between them made evident. Developments in this paper draw upon the non-equilibrium statistical mechanics of Irving & Kirkwood and Noll, together with spatial averaging techniques. Extensions of the early work of Irving & Kirkwood to include multibody potentials and a generalization of the lemmas of Noll to include non-straight bonds are incorporated. Connections to the direct spatial averaging - proach of Murdoch and Hardy are exposed and the troublesome sources of non-uniqueness of the stress tensor are identi ed. Finally, numerical experiments based on molecular - namics and lattice statics are reported. These contrast the various de nitions of stress, - cluding convergence questions related to the size of the domain over which spatial averaging is performed. It is natural to wonder about the connection between works focused on the microscopic foundation of stress and more kinematically-focused works, such as those of Ericksen, P- teri, and Zanzotto, which emphasize the utility of and explore the validity of the Cauchy– Born rule. Podio-Guidugli’s paper, “On (Andersen–)Parrinello–Rahman Molecular Dyn- ics, the Related Metadynamics, and the Use of the Cauchy–Born Rule,” discusses scale bridging between molecular dynamics and continuum mechanics for Parrinello–Rahman molecular dynamics.

Zielgruppe

Research

Autoren/Hrsg.

Fried, E.

Fosdick, Roger

Fachgebiete

• Technische Wissenschaften Maschinenbau | Werkstoffkunde Technische Mechanik | Werkstoffkunde Kontinuumsmechanik
• Naturwissenschaften Physik Angewandte Physik Statistische Physik, Dynamische Systeme
• Naturwissenschaften Physik Mechanik

Inhaltsverzeichnis

Foreword.- Translation of Walter Noll’s “Derivation of the Fundamental Equations of Continuum Thermodynamics from Statistical Mechanics”.- Thoughts on the Concept of Stress.- On Molecular Modelling and Continuum Concepts.- A Unified Interpretation of Stress in Molecular Systems.- On (Andersen–)Parrinello–Rahman Molecular Dynamics, the Related Metadynamics, and the Use of the Cauchy–Born Rule.